منابع مشابه
Birationally rigid Fano hypersurfaces
We prove that a smooth Fano hypersurface V = V M ⊂ P M , M ≥ 6, is birationally superrigid. In particular, it cannot be fibered into uniruled varieties by a non-trivial rational map and each birational map onto a minimal Fano variety of the same dimension is a biregular isomorphism. The proof is based on the method of maximal singularities combined with the connectedness principle of Shokurov a...
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We prove the birational superrigidity and the nonrationality of a cyclic triple cover of P branched over a nodal hypersurface of degree 3n for n ≥ 2. In particular, the obtained result solves the problem of the birational superrigidity of smooth cyclic triple spaces. We also consider certain relevant problems.
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then V is a primitive Fano variety of dimensionM , that is, Pic V = ZKV and (−KV ) is ample. The purpose of this note is to sketch a proof of the following Theorem 1. A general (in the sense of Zariski topology) variety V is birationally superrigid. In particular, V admits no non-trivial structures of a rationally connected fibration, any birational map V 99K V ♯ onto a Fano variety with Q-fact...
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We give a brief survey of the concept of birational rigidity, from its origins in the two-dimensional birational geometry, to its current state. The main ingredients of the method of maximal singularities are discussed. The principal results of the theory of birational rigidity of higher-dimensional Fano varieties and fibrations are given and certain natural conjectures are formulated.
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In this paper we study del Pezzo fibrations z : X → P1 of degree 1 and 2 such that X is smooth, rk Pic(X) = 2 and K2 X ∈ NE(X). These are examples of smooth birationally rigid 3-fold Mori fibre spaces. We describe all birational transformations of the 3-fold X into elliptic fibrations, fibrations of surfaces of Kodaira dimension zero, and canonical Fano 3-folds. Let X be a smooth 3-fold1 of Pic...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1915
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s001309150003755x